Validation of a modal method by use of an appropriate static potential for a plate coupled to a water-filled cavity

This paper deals with the validation of a modal projection method for the low-frequency vibroacoustic response of an elastic structure coupled to a cavity filled with a dense compressible fluid (water).When using a modal approach for internal vibroacoustic problems with heavy fluids, it is shown that a formulation with internal pressure is not correct because it does not take into account the zero-frequency static solutions of the fluid.It is better to use the internal displacement potential involving both the static displacement potential and static pressure terms, although the static displacement potential must be evaluated very carefully. For that purpose, the proposed modal method is validated by comparisons with experiments, a fully analytical solution and a medium-frequency numerical approach, for the case of an elastic rectangular plate coupled to a water-filled parallelepipedic cavity.The validation of the method is focused on the evaluation of the first resonant frequencies of the coupled system, the vibratory response of the plate and the acoustic pressure inside the cavity for a large frequency band.